@inproceedings{10.1007/3-540-54522-0_99,
    Abstract = {In this paper we study the problem of determining whether two points lie in the same connected component of a semi-algebraic set S. Although we are mostly concerned with sets S ⊑ Rn, our algorithm can also decide if points in an arbitrary set S ⊑ Rncan be joined by a semi-algebraic path, for any real closed field R. Our algorithm computes a one-dimensional semi-algebraic subset ℜ(S) of S (actually of an embedding of S in a space {\$}{\$}{\backslash}hat R^n {\$}{\$}for a certain real extension field {\$}{\$}{\backslash}hat R{\$}{\$}of the given field R. ℜ(S) is called the roadmap of S. Our construction uses the original roadmap algorithm described in [Can88a], [Can88b] which worked only for compact, regularly stratified sets.},
    Address = {Berlin, Heidelberg},
    Author = {Canny, J. F.},
    BookTitle = {Applied Algebra, Algebraic Algorithms and Error-Correcting Codes},
    Editor = {Mattson, Harold F. and Mora, Teo and Rao, T. R. N.},
    File = {Computing Roadmaps of General Semi-Algebraic Sets - road93 - a.pdf},
    ISBN = {978-3-540-38436-6},
    Pages = {94--107},
    Publisher = {Springer Berlin Heidelberg},
    Title = {Computing roadmaps of general semi-algebraic sets},
    Year = {1991},
    date-added = {2022-11-26 17:15:28 +0100},
    date-modified = {2022-11-26 17:15:28 +0100},
    doi = {10.1007/3-540-54522-0_99}
}

@inproceedings{10.1007/3-540-54522-0_99, Abstract = {In this paper we study the problem of determining whether two points lie in the same connected component of a semi-algebraic set S. Although we are mostly concerned with sets S ⊑ Rn, our algorithm can also decide if points in an arbitrary set S ⊑ Rncan be joined by a semi-algebraic path, for any real closed field R. Our algorithm computes a one-dimensional semi-algebraic subset ℜ(S) of S (actually of an embedding of S in a space {\$}{\$}{\backslash}hat R^n {\$}{\$}for a certain real extension field {\$}{\$}{\backslash}hat R{\$}{\$}of the given field R. ℜ(S) is called the roadmap of S. Our construction uses the original roadmap algorithm described in [Can88a], [Can88b] which worked only for compact, regularly stratified sets.}, Address = {Berlin, Heidelberg}, Author = {Canny, J. F.}, BookTitle = {Applied Algebra, Algebraic Algorithms and Error-Correcting Codes}, Editor = {Mattson, Harold F. and Mora, Teo and Rao, T. R. N.}, File = {Computing Roadmaps of General Semi-Algebraic Sets - road93 - a.pdf}, ISBN = {978-3-540-38436-6}, Pages = {94--107}, Publisher = {Springer Berlin Heidelberg}, Title = {Computing roadmaps of general semi-algebraic sets}, Year = {1991}, date-added = {2022-11-26 17:15:28 +0100}, date-modified = {2022-11-26 17:15:28 +0100}, doi = {10.1007/3-540-54522-0_99} }